# FlowState: Sampling-Rate-Equivariant Time-Series Forecasting

arXiv: https://arxiv.org/abs/2508.05287 · HTML: https://mlsanity.com/paper/2508.05287/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 33 references that are in the map.
- First posted on arXiv 7 Aug 2025.

## Builds on (most cited first, 25 of 25)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers](https://mlsanity.com/paper/2110.13985/) (2021)
- [HiPPO: Recurrent Memory with Optimal Polynomial Projections](https://mlsanity.com/paper/2008.07669/) (2020)
- [Recurrent Neural Networks for Multivariate Time Series with Missing Values](https://mlsanity.com/paper/1606.01865/) (2016)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [xLSTM: Extended Long Short-Term Memory](https://mlsanity.com/paper/2405.04517/) (2024)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [Sundial: A Family of Highly Capable Time Series Foundation Models](https://mlsanity.com/paper/2502.00816/) (2025)
- [Tiny Time Mixers (TTMs): Fast Pre-trained Models for Enhanced Zero/Few-Shot Forecasting of Multivariate Time Series](https://mlsanity.com/paper/2401.03955/) (2024)
- [How to Train Your HiPPO: State Space Models with Generalized Orthogonal Basis Projections](https://mlsanity.com/paper/2206.12037/) (2022)
- [TiRex: Zero-Shot Forecasting Across Long and Short Horizons with Enhanced In-Context Learning](https://mlsanity.com/paper/2505.23719/) (2025)
- [Is Mamba Effective for Time Series Forecasting?](https://mlsanity.com/paper/2403.11144/) (2024)
- [Vision Mamba: A Comprehensive Survey and Taxonomy](https://mlsanity.com/paper/2405.04404/) (2024)
- [Toto: Time Series Optimized Transformer for Observability](https://mlsanity.com/paper/2407.07874/) (2024)
- [LightGTS: A Lightweight General Time Series Forecasting Model](https://mlsanity.com/paper/2506.06005/) (2025)
- [Mamba in Vision: A Comprehensive Survey of Techniques and Applications](https://mlsanity.com/paper/2410.03105/) (2024)

## Built on by (most cited first, 8 of 8)

- [EXAONE Finance 1.0: An Attention-free Time Series Foundation Model for Financial Time Series](https://mlsanity.com/paper/2609.04239/) (2026)
- [Forecast Collapse in Time-Series Foundation Models](https://mlsanity.com/paper/2608.14106/) (2026)
- [TinyCast: Probabilistic Zero-Shot Forecasting with Computed Periodicity](https://mlsanity.com/paper/2608.15767/) (2026)
- [EXAONE Demand 1.0: A Time Series Foundation Model for Demand Forecasting](https://mlsanity.com/paper/2609.30880/) (2026)
- [Fracast-0: Fractal Weight Sharing for a Time Series Foundation Model with Only 85K Parameters](https://mlsanity.com/paper/2609.32209/) (2026)
- [Self-Evolving Time-Series Forecasting Agents with Episodic Memory and Online Policy Learning](https://mlsanity.com/paper/2609.32689/) (2026)
- [OpenTSLM TeeMoE: A Unified Time-Series Language Model for Forecasting, Contextual Prediction, and Reasoning](https://mlsanity.com/paper/2609.40265/) (2026)
- [A Unified Scaling Law for Time Series Foundation Models](https://mlsanity.com/paper/2610.05269/) (2026)

## Abstract (arXiv)

Existing time series foundation models (TSFMs), often based on transformer variants, lack adaptability to different sampling rates, struggle with generalization across varying context and target lengths, and are computationally inefficient. We introduce FlowState, a novel TSFM architecture that achieves sampling-rate-equivariant forecasting through a unified design that pairs a state space model (SSM) encoder with a functional basis decoder (FBD). This design enables continuous-time modeling and dynamic time-scale adjustment, allowing FlowState to inherently generalize across all possible temporal resolutions, and dynamically adjust the forecasting horizons without retraining. We further propose an efficient pretraining strategy that improves robustness and accelerates training. Despite being one of the smallest TSFMs, FlowState achieves state-of-the-art results on the widely used GIFT-Eval benchmark, while demonstrating superior adaptability to unseen sampling rates. Our detailed analyses confirm the effectiveness of its components, and we demonstrate its unique ability to adapt to varying input sampling rates.